Constructing genetic and physical maps for all the human chromosomes are fundamental aims of the Human Genome Project, and the promise to map and identify genes for human diseases is a principal reason why the Genome Project has widespread support. Efficient statistical methods help to insure that these goals are met in a timely, cost-effective manner. In this proposal, the investigators address a set of methodological problems that arise in radiation hybrid and linkage map construction, and the mapping of human disease genes by linkage and association analysis. First, the investigators will develop and test methods for linkage mapping of genes for complex human disease. The investigators extend multipoint affected sib pair (ASP) linkage analysis to allow explicitly for genotyping error and assess the value of this extension, evaluate the robustness of ASP linkage analysis to errors in order and intermarker distance in genetic maps, and examine the variability of the multipoint lod score function in the presence of a disease locus to address the issue of replication of linkage findings. Second, the investigators will develop a Bayesian method of point and interval estimation of marker position for radiation hybrid and linkage mapping that takes into account ordering uncertainty. Third, the investigators will develop family-based association methods for gene mapping based on a discordant sib pair (DSP) design and evaluate an extension to parent-offspring trio association methods that uses both affected and unaffected offspring. Fourth, the investigators will develop, test, distribute, and support computer software based on the methods that arise from the other goals of this project, and will continue to update, distribute, and support their current software including SIMLINK, RHMAP, RELPAIR, and several modules of the MENDEL package. Fifth, the investigators will continue to be opportunistic in identifying and addressing important statistical modeling and analysis problems that are related to the other goals of this project.